Statistical learnability of nuclear masses

After more than 80 years from the seminal work of Weizs\"acker and the liquid drop model of the atomic nucleus, deviations from experiments of mass models ($\sim$ MeV) are orders of magnitude larger than experimental errors ($\lesssim$ keV). Predicting the mass of atomic nuclei with precision is extremely challenging. This is due to the non--trivial many--body interplay of protons and neutrons in nuclei, and the complex nature of the nuclear strong force. Statistical theory of learning will be used to provide bounds to the prediction errors of model trained with a finite data set. These bounds are validated with neural network calculations, and compared with state of the art mass models. Therefore, it will be argued that the nuclear structure models investigating ground state properties explore a system on the limit of the knowledgeable, as defined by the statistical theory of learning

Unified description of structure and reactions: implementing the Nuclear Field Theory program

The modern theory of the atomic nucleus results from the merging of the liquid drop (Niels Bohr and Fritz Kalckar) and of the shell model (Marie Goeppert Meyer and Axel Jensen), which contributed the concepts of collective excitations and of independent-particle motion respectively. The unification of these apparently contradictory views in terms of the particle-vibration (rotation) coupling (Aage Bohr and Ben Mottelson) has allowed for an ever increasingly complete, accurate and detailed description of the nuclear structure, Nuclear Field Theory (NFT, developed by the Copenhagen-Buenos Aires collaboration) providing a powerful quantal embodiment. In keeping with the fact that reactions are not only at the basis of quantum mechanics (statistical interpretation, Max Born) , but also the specific tools to probe the atomic nucleus, NFT is being extended to deal with processes which involve the continuum in an intrinsic fashion, so as to be able to treat them on an equal footing with those associated with discrete states (nuclear structure). As a result, spectroscopic studies of transfer to continuum states could eventually use at profit the NFT rules, extended to take care of recoil effects. In the present contribution we review the implementation of the NFT program of structure and reactions, setting special emphasis on open problems and outstanding predictions.Comment: submitted to Physica Scripta to the Focus Issue on Nuclear Structure: Celebrating the 1975 Nobel Priz

Reaction mechanism of two-neutron transfer in DWBA

We present a brief introduction to the second order DWBA reaction formalism which we have used to perform the theoretical analysis of two–nucleon transfer reactions induced both by heavy and light ions. We also show an example of such a calculation, emphasizing the connection between the structure aspects of the prob- lem and the resulting predicted two–neutron transfer cross section. The calculations were carried out making use of software specifically developed for this purpose. It includes sequential, simultaneous and non–orthogonality contributions to the process. Microscopic form factors are used which take into account the relevant structure aspects of the process, such as the nature of the single–particle wavefunctions, the spectroscopic factors, and the interaction potential responsible for the transfer. Overall agreement with the experimental absolute values of the differential cross section is obtained without any free paramete

Quantitative study of coherent pairing modes with two-neutron transfer: Sn isotopes

Pairing rotations and pairing vibrations are collective modes associated with a field, the pair field, which changes the number of particles by two. Consequently, they can be studied at profit with the help of two-particle transfer reactions in superfluid and in normal nuclei, respectively. The advent of exotic beams has opened, for the first time, the possibility to carry out such studies in medium heavy nuclei, within the same isotopic chain. The case studied in the present paper is that of the Sn isotopes [essentially from closed (Z=N=50) to closed (Z=50, N=82) shells]. The static and dynamic off-diagonal, long-range order phase coherence in gauge space displayed by pairing rotations and vibrations, respectively, leads to coherent states which behave almost classically. Consequently, these modes are amenable to an accurate nuclear structure description in terms of simple models containing the right physics, in particular, BCS plus quasiparticle random-phase approximation and Hartree-Fock mean field plus random-phase approximation, respectively. The associated two-nucleon transfer spectroscopic amplitudes predicted by such model calculations can thus be viewed as essentially "exact." This fact, together with the availability of optical potentials for the different real and virtual channels involved in the reactions considered, namely A +2Sn+p, A+1Sn+d, and ASn+t, allows for the calculation of the associated absolute cross sections without, arguably, free parameters. The numerical predictions of the absolute differential cross sections, obtained making use of the above-mentioned nuclear structure and optical potential inputs, within the framework of second-order distorted-wave Born approximation, taking into account simultaneous, successive, and nonorthogonality contributions, provide, within experimental errors in general, and below 10% uncertainty in particular, an overall account of the experimental findings for all of the measured A+2Sn(p,t)ASn(gs) reactions, for which absolute cross sections have been reported to date

Mineralogy of the scheelite-bearing ores of Monte Tamara, SW Sardinia: insights for the evolution of a Late Variscan W–Sn skarn system

Southwestern Sardinia, Italy, hosts several skarn, W–Sn–Mo greisen and hydrothermal deposits related to a 289±1 Ma Late Variscan granite suite. Among them, the most representative scheelite-bearing skarns belong to the San Pietro and Sinibidraxiu localities, in the Monte Tamara area, Sulcis region. The San Pietro deposit is a typical calc-silicate skarn whereas Sinibidraxiu is a sharply bounded orebody hosted in a marble unit. Optical petrographic observations and compositional data of major and trace elements were obtained for samples from both localities. San Pietro data suggests evolution from an oxidising prograde skarn stage (andradite–diopside, hematite and scheelite), to progressively more reducing conditions from the early retrograde (magnetite–cassiterite) to the late sulfide stage (arsenopyrite, stannite, molybdenite, Bi sulfosalts and Zn–Cu–Pb–Fe sulfides); Sinibidraxiu has diffuse carbonate–quartz intergrowths pseudomorphic over an early mineral assemblage with fibrous habit, followed by abundant ore mineral precipitation under reducing conditions (scheelite, arsenopyrite and Pb–Zn–Cu–Fe sulfides). Geothermometers indicate a comprehensive temperature range of 460–270°C for the sulfide stages of both deposits. The differences between the two deposits might be controlled by the distance from the source intrusion coupled with the different reactivity of the host rocks. The San Pietro mineralogy represents a more proximal skarn, contrasting with more distal mineralogical and chemical features characterising the Sinibidraxiu orebody (lack of Mo–Sn–Bi phases; LREE–MREE–HREE signature of scheelite). This investigation contributes for the first time to the identification of a W–Sn skarn system in SW Sardinia, thereby suggesting the Monte Tamara area and its surroundings as favourable for further exploration

Classification of Cellular Automata based on Statistical Mechanics

Cellular automata are a set of computational models in discrete space that have a discrete time evolution defined by neighbourhood rules. They are used to simulate many complex systems in physics and science in general. In this work, statistical mechanics and thermodynamics are used to analyse a large set of outer totalistic two-dimensional cellular automata. Thermodynamic variables and potentials are derived and computed according to three different approaches to determine if a cellular automaton rule is representing a system akin to the ideal gas, in or out of the thermodynamical equilibrium. It is suggested that this classification is sufficiently robust and predictive of interesting properties for particular set of rules.Comment: 24 Pages, 7 Figure